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Representation of feedback operators for parabolic control problems

Author: Belinda B. King
Journal: Proc. Amer. Math. Soc. 128 (2000), 1339-1346
MSC (1991): Primary 35K05, 47B99, 49J20
Published electronically: February 7, 2000
MathSciNet review: 1709756
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In this paper we present results on existence and regularity of integral representations of feedback operators arising from parabolic control problems. The existence of such representations is important for the design of low order compensators and in the placement of sensors. This paper extends earlier results of J. A. Burns and B. B. King to problems with $N$ spatial dimensions.

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Additional Information

Belinda B. King
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605
Address at time of publication: Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0531

Keywords: Integral representation, Riccati operator, parabolic control problem
Received by editor(s): August 17, 1995
Received by editor(s) in revised form: May 17, 1996
Published electronically: February 7, 2000
Additional Notes: This research was supported in part by the Air Force Office of Scientific Research under grant F49620-93-1-0280 while the author was a visiting scientist at the Air Force Center for Optimal Design and Control, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061–0531, and by the National Science Foundation under grant DMS-9409506.
Communicated by: John A. Burns
Article copyright: © Copyright 2000 American Mathematical Society